Kernel Filters
In signal and data processing, and particularly, in image speech processing, kernel filters are frequently applied to input data to produce enhanced output data. A kernel filter works by applying a function to every point in a set of data. In the case of images, the points are pixels.
Typically, a kernel filter includes a kernel and a function defined on the kernel. The kernel, which is often a rectangular area of pixels in a 2D image, specifies the region of support for the function. The function is usually in the form of a matrix of filter coefficients. The coefficients of the matrix are the multiplication factors that determine the contribution of each point within the kernel, to generate a response of the filter. After all the underlying input data have been multiplied by the filter coefficients, the response at the current point is determined by taking the sum of the products. By selecting different kernel functions, different types of filtering can be performed.
Filtering can be computationally demanding. Therefore, conventional approaches try to break down the original kernel into a convolution of smaller kernels using. However, a large number of multiplications are needed to carry out all of the convolutions with a large set of kernels.
Filtering can be accelerated by substituting pixels in the kernels with the central pixel of a code vector. A sum-box filter approximates a large kernel linear filter to a factor by the sum of the translated outputs of sum-box filters. That technique is limited to Gaussian filters. In a fuzzy domain, a recursive and separable low-pass filter can be used. However, that method is only applicable to symmetric filters. There are also methods to decompose non-linear filters into a sum of separable one-dimensional filters or cascaded representations. That can be done by either an eigenvalue expansion of the 2D kernel, or by an application of singular value decomposition.
Filter can be adapted to a specific orientation by making a linear combination of basis filters. Another method generates a finite basis, which approximates an anisotropic Gaussian filter. By taking advantage of the separability of the 2D Gaussian function, an anisotropic Gaussian kernel can be decomposed into a 1D Gaussian filter followed by another filter in a nonorthogonal direction.
Bilateral Filters
A bilateral, filter combines a spatial filter with a range filter. The coefficients of the spatial filter vary according to distances, and the coefficients of the range filter vary according intensities. Because the range filter is non-linear, bilateral filtering is computationally demanding. One method for bilateral filtering uses as a single iteration of the diagonal normalized steepest descent algorithm. Another method derives criteria for down sampling in space and intensity to accelerate the bilateral filter. Other methods use reconfigurable hardware or processor adapted software to accelerate the filtering process.
The known methods for spatial filtering are either restricted to Gaussian kernels or linear functions. Bilateral filtering methods tend to decrease the amount of data by down sampling and result in a coarse approximation. It is desired to provide a bilateral filter method that is accurate and fast.